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Diskretnyi Analiz i Issledovanie Operatsii, 2011, Volume 18, Issue 5, Pages 38–53 (Mi da664)  

This article is cited in 4 scientific papers (total in 4 papers)

Thin circulant matrixes and lower bounds on complexity of some Boolean operators

M. I. Grinchuk, I. S. Sergeev

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (308 kB) Citations (4)
References:
Abstract: Lower estimate $\Omega(\frac{k+l}{k^2l^2}N^{2-\frac{k+l+2}{kl}})$ of the maximal possible weight of a $(k,l)$-thin (that is, free of all-ones' submatrixes of size $k\times l$) circulant matrix of order $N$ is proved. The estimate is close to the known estimate corresponding to the class of all $(k,l)$-thin matrixes. As a consequence, new estimates of several complexity measures of Boolean sums' systems and a lower estimate $\Omega(N^2\log^{-6}N)$ of monotone complexity of a Boolean convolution of order $N$ are obtained. Ill. 1, bibliogr. 11.
Keywords: complexity, circulant matrix, thin matrix, Zarankiewicz problem, monotone circuit, rectifier circuit, Boolean sum, Boolean convolution.
Received: 27.01.2011
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: M. I. Grinchuk, I. S. Sergeev, “Thin circulant matrixes and lower bounds on complexity of some Boolean operators”, Diskretn. Anal. Issled. Oper., 18:5 (2011), 38–53
Citation in format AMSBIB
\Bibitem{GriSer11}
\by M.~I.~Grinchuk, I.~S.~Sergeev
\paper Thin circulant matrixes and lower bounds on complexity of some Boolean operators
\jour Diskretn. Anal. Issled. Oper.
\yr 2011
\vol 18
\issue 5
\pages 38--53
\mathnet{http://mi.mathnet.ru/da664}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2918328}
\zmath{https://zbmath.org/?q=an:1249.68087}
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  • https://www.mathnet.ru/eng/da/v18/i5/p38
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретный анализ и исследование операций
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    Abstract page:529
    Full-text PDF :131
    References:46
    First page:8
     
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